Optimal packings of bounded degree trees

We prove that if T1,…,Tn is a sequence of bounded degree trees such that Ti has i vertices, then Kn has a decomposition into T1,…,Tn. This shows that the tree packing conjecture of Gyárfás and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first o(n) trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields decompositions of dense quasi-random graphs into suitable families of bounded degree graphs. Our proofs involve Szemerédi's regularity lemma, results on Hamilton decompositions of robust expanders, random walks, iterative absorption as well as a recent blow-up lemma for approximate decompositions

Spartan Daily, November 30, 1945

Volume 34, Issue 39https://scholarworks.sjsu.edu/spartandaily/3669/thumbnail.jp

On the Six-Cornered Snowflake

On the Six-Cornered Snowflake, named after Johannes Kepler’s 1611 essay on geometrically covering surfaces, is both the title of both my final thesis work and essay. Beginning with an inquiry into the nature of hand-made object as intrinsically valuable, my earlier sculptural work surrounding quilting is broken down and considered as a form of reverence for the American object. This is partly achieved through a comparison to traditional Japanese packing techniques and how my own assembly mirrors and converses with the graceful and sensitive packing of Japanese hand-made goods. Early 20th-century flight experiments are also hand-made objects of interest. Their history as tools, but more importantly as failures, introduces more clearly the importance and fascination I have with obsolete objects. The history of these machines, namely Alexander Graham Bell’s tetrahedral kites, serves as the basis for an exploratory body of drawings used to highlight and reappropriate the obsolete machines. These drawings, in a similar fashion to artists Helen Mirra and Roni Horn, approach empirical science with a poetic lens. Through iteration and trust, the body of work orients itself towards a faith in mathematical systems and their miraculous adaptability, ultimately serving as the poetic crux of the work

Spartan Daily, February 25, 1936

Volume 24, Issue 89https://scholarworks.sjsu.edu/spartandaily/2417/thumbnail.jp

Volume 55, Number 1 - November 1975

Volume 55, Number 1 - November 1975. 27 pages including covers and advertisements. Contributions Slonina, Patricia L. Taking Out the Boat Prevey, Debra impressions: fall Tremblay, Bill Janis Joplin & The Invention of Barbed Wire Schaffer, Dora Bounty Hunter Coskren, Thomas M., O.P. A Better Parlor: Setting as Meaning in Henry James\u27s The Bostonians Maciag, Drew My Heart Is A Japanese Garden Like Paper Blossoms In A Chinese Sunset McCrorie, Edward Big Tree Talk Avakian, Robert M. Crystal Sphericon Windows Gray, Jereld Complaint Picararo, Steve Rousseau! Rousseau! Selley, April Love Poem Perel, Jane Lunin Bass Head Washed Up on Shore at Galilee, R.I., July 16, 1975 Woody, Michael M. The Elegy Logan, S. What The Fish Sees Photograph McCrorie, Edwar

Optimal packings of bounded degree trees

We prove that if T1,…,Tn is a sequence of bounded degree trees such that Ti has i vertices, then Kn has a decomposition into T1,…,Tn. This shows that the tree packing conjecture of Gyárfás and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first o(n) trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields decompositions of dense quasi-random graphs into suitable families of bounded degree graphs. Our proofs involve Szemerédi's regularity lemma, results on Hamilton decompositions of robust expanders, random walks, iterative absorption as well as a recent blow-up lemma for approximate decompositions

Interview with Theodore Ozawa

Theodore Ozawa, eldest of six children, was born in 1932, in Wahiawa, Kaua‘i, Hawai‘i. His parents were immigrants from Yamanashi-ken, Japan. His father, Yoshikiyo Ozawa, a Soto Mission minister whose Buddhist name was Gijo, arrived with his wife, Hanako, to assume the position of minister at Zenshuji in Wahiawa, Kaua‘i, in 1931. Besides meeting the religious needs of the Japanese community at surrounding McBryde Sugar Company plantation, the Ozawas filled educational and cultural needs. Yoshikiyo Ozawa served as principal of the Japanese-language school; Hanako Ozawa served as a classroom teacher and instructor in sewing and flower arrangement. Yoshikiyo Ozawa also organized classes in martial arts. With the outbreak of war, Yoshikiyo Ozawa was removed from the minister’s residence on December 7, 1941. Initially held at a facility on Kaua‘i, he was later moved to Sand Island Detention Center and to the U.S. Mainland. The Ozawa family—Hanako and four children, Theodore, Donald, Gordon, and Clara—were placed in Jerome War Relocation Center in early 1943. Separated from their father who was held in facilities elsewhere, including Camp Livingston, Louisiana, they were not reunited until all were sent to Tule Lake Segregation Center, California in summer 1944. There, Yoshikiyo Ozawa worked in an office while Hanako Ozawa helped in the mess hall. Their fifth child, Walter, was born at Tule Lake. Allowed to return to the islands in 1945, the Ozawas returned to Zenshuji where they remained until they were transferred to Taiyoji on the island of O‘ahu in 1951. Theodore Ozawa, who earned degrees at the University of Hawai‘i, taught at Willamette University until his retirement in 1994. He has two children and one grandchild